Unraveling motion in proteins by combining NMR relaxometry and molecular dynamics simulations: A case study on ubiquitin.

Nuclear magnetic resonance (NMR) relaxation experiments shine light onto the dynamics of molecular systems in the picosecond to millisecond timescales. As these methods cannot provide an atomically resolved view of the motion of atoms, functional groups, or domains giving rise to such signals, relaxation techniques have been combined with molecular dynamics (MD) simulations to obtain mechanistic descriptions and gain insights into the functional role of side chain or domain motion. In this work, we present a comparison of five computational methods that permit the joint analysis of MD simulations and NMR relaxation experiments. We discuss their relative strengths and areas of applicability and demonstrate how they may be utilized to interpret the dynamics in MD simulations with the small protein ubiquitin as a test system. We focus on the aliphatic side chains given the rigidity of the backbone of this protein. We find encouraging agreement between experiment, Markov state models built in the χ1/χ2 rotamer space of isoleucine residues, explicit rotamer jump models, and a decomposition of the motion using ROMANCE. These methods allow us to ascribe the dynamics to specific rotamer jumps. Simulations with eight different combinations of force field and water model highlight how the different metrics may be employed to pinpoint force field deficiencies. Furthermore, the presented comparison offers a perspective on the utility of NMR relaxation to serve as validation data for the prediction of kinetics by state-of-the-art biomolecular force fields.

Exploring protein-ligand binding affinity prediction with electron density-based geometric deep learning.

Rational structure-based drug design relies on accurate predictions of protein-ligand binding affinity from structural molecular information. Although deep learning-based methods for predicting binding affinity have shown promise in computational drug design, certain approaches have faced criticism for their potential to inadequately capture the fundamental physical interactions between ligands and their macromolecular targets or for being susceptible to dataset biases. Herein, we propose to include bond-critical points based on the electron density of a protein-ligand complex as a fundamental physical representation of protein-ligand interactions. Employing a geometric deep learning model, we explore the usefulness of these bond-critical points to predict absolute binding affinities of protein-ligand complexes, benchmark model performance against existing methods, and provide a critical analysis of this new approach. The models achieved root-mean-squared errors of 1.4-1.8 log units on the PDBbind dataset, and 1.0-1.7 log units on the PDE10A dataset, not indicating significant advantages over benchmark methods, and thus rendering the utility of electron density for deep learning models context-dependent. The relationship between intermolecular electron density and corresponding binding affinity was analyzed, and Pearson correlation coefficients r > 0.7 were obtained for several macromolecular targets.

Combining IC50 or Ki Values from Different Sources Is a Source of Significant Noise.

As part of the ongoing quest to find or construct large data sets for use in validating new machine learning (ML) approaches for bioactivity prediction, it has become distressingly common for researchers to combine literature IC50 data generated using different assays into a single data set. It is well-known that there are many situations where this is a scientifically risky thing to do, even when the assays are against exactly the same target, but the risks of assays being incompatible are even higher when pulling data from large collections of literature data like ChEMBL. Here, we estimate the amount of noise present in combined data sets using cases where measurements for the same compound are reported in multiple assays against the same target. This approach shows that IC50 assays selected using minimal curation settings have poor agreement with each other: almost 65% of the points differ by more than 0.3 log units, 27% differ by more than one log unit, and the correlation between the assays, as measured by Kendall's τ, is only 0.51. Requiring that most of the assay metadata in ChEMBL matches ("maximal curation") in order to combine two assays improves the situation (48% of the points differ by more than 0.3 log units, 13% by more than one log unit, and Kendall's τ is 0.71) at the expense of having smaller data sets. Surprisingly, our analysis shows similar amounts of noise when combining data from different literature Ki assays. We suggest that good scientific practice requires careful curation when combining data sets from different assays and hope that our maximal curation strategy will help to improve the quality of the data that are being used to build and validate ML models for bioactivity prediction. To help achieve this, the code and ChEMBL queries that we used for the maximal curation approach are available as open-source software in our GitHub repository, https://github.com/rinikerlab/overlapping_assays.

Experimental and Theoretical Studies on the Reactions of Aliphatic Imines with Isocyanates.

In the context of a project aiming at the replacement of the 3-substituted ß-lactam ring in classical ß-lactam antibiotics by an N(3)-acyl-1,3-diazetidinone moiety, we have investigated the reaction of isocyanates with imines derived from allyl glycinate and differently substituted propionaldehydes. Imines of aromatic aldehydes with anilines have been reported to react with acyl isocyanates to give 1,3-diazetidinones or 2,3-dihydro-4H-1,3,5-oxadiazin-4-ones, via [2+2] or [4+2] cycloaddition, respectively. However, neither of these products was formed with imines derived from allyl glycinate and 2-(mono)methyl propionaldehydes. α,α-Dimethylation of the imine enabled the [4+2] cycloaddition pathway, but the desired 1,3-diazetidinone products were not observed. Surprisingly, the imines obtained from thioesters of 2,2-dimethyl 3-oxo propionic acid reacted with aryl isocyanates or with benzyl isocyanate to give 5,5-dimethyl-2,4-dioxo-6-(aryl-/alkylthio)tetrahydropyrimidines, via thiol displacement and re-addition to a putative six-membered iminium intermediate. These experimental results obtained for the reactions could be rationalized by DFT calculations. In addition, we have shown that N(3)-acyl-1,3-diazetidinone and 2,3-dihydro-4H-1,3,5-oxadiazin-4-one products can be distinguished based on experimental IR data in combination with theoretical reference spectra employing the IR spectra alignment (IRSA) algorithm. This discrimination was not possible by means of 1 H, 13 C, or 15 N NMR spectroscopy.

SIMPD: an algorithm for generating simulated time splits for validating machine learning approaches.

Time-split cross-validation is broadly recognized as the gold standard for validating predictive models intended for use in medicinal chemistry projects. Unfortunately this type of data is not broadly available outside of large pharmaceutical research organizations. Here we introduce the SIMPD (simulated medicinal chemistry project data) algorithm to split public data sets into training and test sets that mimic the differences observed in real-world medicinal chemistry project data sets. SIMPD uses a multi-objective genetic algorithm with objectives derived from an extensive analysis of the differences between early and late compounds in more than 130 lead-optimization projects run within the Novartis Institutes for BioMedical Research. Applying SIMPD to the real-world data sets produced training/test splits which more accurately reflect the differences in properties and machine-learning performance observed for temporal splits than other standard approaches like random or neighbor splits. We applied the SIMPD algorithm to bioactivity data extracted from ChEMBL and created 99 public data sets which can be used for validating machine-learning models intended for use in the setting of a medicinal chemistry project. The SIMPD code and simulated data sets are available under open-source/open-data licenses at github.com/rinikerlab/molecular_time_series.

Simulation of aqueous solutes using the adaptive solvent-scaling (AdSoS) scheme.

The Adaptive Solvent-Scaling (AdSoS) scheme [J. Chem. Phys. 155 (2021) 094107] is an adaptive-resolution approach for performing simulations of a solute embedded in a fine-grained (FG) solvent region surrounded by a coarse-grained (CG) solvent region, with a continuous FG ↔ CG switching of the solvent resolution across a buffer layer. Instead of relying on a distinct CG solvent model, AdSoS is based on CG models defined by a dimensional scaling of the FG solvent by a factor s, accompanied by the s-dependent modulation of its mass and interaction parameters. The latter changes are designed to achieve an isomorphism between the dynamics of the FG and CG models, and to preserve the dispersive and dielectric solvation properties of the solvent with respect to a solute at FG resolution. As a result, the AdSoS scheme minimizes the thermodynamic mismatch between different regions of the adaptive-resolution system. The present article generalizes the scheme initially introduced for a pure atomic liquid in slab geometry to more practically relevant situations involving (i) a molecular dipolar solvent (e.g., water); (ii) a radial geometry (i.e., spherical rather than planar layers); and (iii) the inclusion of a solute (e.g., water molecule, dipeptide, ion, or ion pair).

Accelerating Alchemical Free Energy Prediction Using a Multistate Method: Application to Multiple Kinases.

Alchemical free-energy methods based on molecular dynamics (MD) simulations have become important tools to identify modifications of small organic molecules that improve their protein binding affinity during lead optimization. The routine application of pairwise free-energy methods to rank potential binders from best to worst is impacted by the combinatorial increase in calculations to perform when the number of molecules to assess grows. To address this fundamental limitation, our group has developed replica-exchange enveloping distribution sampling (RE-EDS), a pathway-independent multistate method, enabling the calculation of alchemical free-energy differences between multiple ligands (N > 2) from a single MD simulation. In this work, we apply the method to a set of four kinases with diverse binding pockets and their corresponding inhibitors (42 in total), chosen to showcase the general applicability of RE-EDS in prospective drug design campaigns. We show that for the targets studied, RE-EDS is able to model up to 13 ligands simultaneously with high sampling efficiency, leading to a substantial decrease in computational cost when compared to pairwise methods.

Hybrid classical/machine-learning force fields for the accurate description of molecular condensed-phase systems.

Electronic structure methods offer in principle accurate predictions of molecular properties, however, their applicability is limited by computational costs. Empirical methods are cheaper, but come with inherent approximations and are dependent on the quality and quantity of training data. The rise of machine learning (ML) force fields (FFs) exacerbates limitations related to training data even further, especially for condensed-phase systems for which the generation of large and high-quality training datasets is difficult. Here, we propose a hybrid ML/classical FF model that is parametrized exclusively on high-quality ab initio data of dimers and monomers in vacuum but is transferable to condensed-phase systems. The proposed hybrid model combines our previous ML-parametrized classical model with ML corrections for situations where classical approximations break down, thus combining the robustness and efficiency of classical FFs with the flexibility of ML. Extensive validation on benchmarking datasets and experimental condensed-phase data, including organic liquids and small-molecule crystal structures, showcases how the proposed approach may promote FF development and unlock the full potential of classical FFs.

DASH: Dynamic Attention-Based Substructure Hierarchy for Partial Charge Assignment.

We present a robust and computationally efficient approach for assigning partial charges of atoms in molecules. The method is based on a hierarchical tree constructed from attention values extracted from a graph neural network (GNN), which was trained to predict atomic partial charges from accurate quantum-mechanical (QM) calculations. The resulting dynamic attention-based substructure hierarchy (DASH) approach provides fast assignment of partial charges with the same accuracy as the GNN itself, is software-independent, and can easily be integrated in existing parametrization pipelines, as shown for the Open force field (OpenFF). The implementation of the DASH workflow, the final DASH tree, and the training set are available as open source/open data from public repositories.

Energy-based clustering: Fast and robust clustering of data with known likelihood functions.

Clustering has become an indispensable tool in the presence of increasingly large and complex datasets. Most clustering algorithms depend, either explicitly or implicitly, on the sampled density. However, estimated densities are fragile due to the curse of dimensionality and finite sampling effects, for instance, in molecular dynamics simulations. To avoid the dependence on estimated densities, an energy-based clustering (EBC) algorithm based on the Metropolis acceptance criterion is developed in this work. In the proposed formulation, EBC can be considered a generalization of spectral clustering in the limit of large temperatures. Taking the potential energy of a sample explicitly into account alleviates requirements regarding the distribution of the data. In addition, it permits the subsampling of densely sampled regions, which can result in significant speed-ups and sublinear scaling. The algorithm is validated on a range of test systems including molecular dynamics trajectories of alanine dipeptide and the Trp-cage miniprotein. Our results show that including information about the potential-energy surface can largely decouple clustering from the sampled density.

Influence of the Fluorophore Mobility on Distance Measurements by Gas-Phase FRET.

Gas-phase Förster resonance energy transfer (FRET) combines mass spectrometry and fluorescence spectroscopy for the conformational analysis of mass-selected biomolecular ions. In FRET, fluorophore pairs are typically covalently attached to a biomolecule using short linkers, which affect the mobility of the dye and the relative orientation of the transition dipole moments of the donor and acceptor. Intramolecular interactions may further influence the range of motion. Yet, little is known about this factor, despite the importance of intramolecular interactions in the absence of a solvent. In this study, we applied transition metal ion FRET (tmFRET) to probe the mobility of a single chromophore pair (Rhodamine 110 and Cu2+) as a function of linker lengths to assess the relevance of intramolecular interactions. Increasing FRET efficiencies were observed with increasing linker length, ranging from 5% (2 atoms) to 28% (13 atoms). To rationalize this trend, we profiled the conformational landscape of each model system using molecular dynamics (MD) simulations. We captured intramolecular interactions that promote a population shift toward smaller donor-acceptor separation for longer linker lengths and induce a significant increase in the acceptor's transition dipole moment. The presented methodology is a first step toward the explicit consideration of a fluorophore's range of motion in the interpretation of gas-phase FRET experiments.

Implicit solvent approach based on generalized Born and transferable graph neural networks for molecular dynamics simulations.

Molecular dynamics simulations enable the study of the motion of small and large (bio)molecules and the estimation of their conformational ensembles. The description of the environment (solvent) has, therefore, a large impact. Implicit solvent representations are efficient but, in many cases, not accurate enough (especially for polar solvents, such as water). More accurate but also computationally more expensive is the explicit treatment of the solvent molecules. Recently, machine learning has been proposed to bridge the gap and simulate, in an implicit manner, explicit solvation effects. However, the current approaches rely on prior knowledge of the entire conformational space, limiting their application in practice. Here, we introduce a graph neural network based implicit solvent that is capable of describing explicit solvent effects for peptides with different compositions than those contained in the training set.

Determining the gas-phase structures of α-helical peptides from shape, microsolvation, and intramolecular distance data.

Mass spectrometry is a powerful technique for the structural and functional characterization of biomolecules. However, it remains challenging to accurately gauge the gas-phase structure of biomolecular ions and assess to what extent native-like structures are maintained. Here we propose a synergistic approach which utilizes Förster resonance energy transfer and two types of ion mobility spectrometry (i.e., traveling wave and differential) to provide multiple constraints (i.e., shape and intramolecular distance) for structure-refinement of gas-phase ions. We add microsolvation calculations to assess the interaction sites and energies between the biomolecular ions and gaseous additives. This combined strategy is employed to distinguish conformers and understand the gas-phase structures of two isomeric α-helical peptides that might differ in helicity. Our work allows more stringent structural characterization of biologically relevant molecules (e.g., peptide drugs) and large biomolecular ions than using only a single structural methodology in the gas phase.

Accounting for Solvation Correlation Effects on the Thermodynamics of Water Networks in Protein Cavities.

Macromolecular recognition and ligand binding are at the core of biological function and drug discovery efforts. Water molecules play a significant role in mediating the protein-ligand interaction, acting as more than just the surrounding medium by affecting the thermodynamics and thus the outcome of the binding process. As individual water contributions are impossible to measure experimentally, a range of computational methods have emerged to identify hydration sites in protein pockets and characterize their energetic contributions for drug discovery applications. Even though several methods model solvation effects explicitly, they focus on determining the stability of specific water sites independently and neglect solvation correlation effects upon replacement of clusters of water molecules, which typically happens in hit-to-lead optimization. In this work, we rigorously determine the conjoint effects of replacing all combinations of water molecules in protein binding pockets through the use of the RE-EDS multistate free-energy method, which combines Hamiltonian replica exchange (RE) and enveloping distribution sampling (EDS). Applications on the small bovine pancreatic trypsin inhibitor and four proteins of the bromodomain family illustrate the extent of solvation correlation effects on water thermodynamics, with the favorability of replacement of the water sites by pharmacophore probes highly dependent on the composition of the water network and the pocket environment. Given the ubiquity of water networks in biologically relevant protein targets, we believe our approach can be helpful for computer-aided drug discovery by providing a pocket-specific and a priori systematic consideration of solvation effects on ligand binding and selectivity.

Lessons for Oral Bioavailability: How Conformationally Flexible Cyclic Peptides Enter and Cross Lipid Membranes.

Cyclic peptides extend the druggable target space due to their size, flexibility, and hydrogen-bonding capacity. However, these properties impact also their passive membrane permeability. As the "journey" through membranes cannot be monitored experimentally, little is known about the underlying process, which hinders rational design. Here, we use molecular simulations to uncover how cyclic peptides permeate a membrane. We show that side chains can act as "molecular anchors", establishing the first contact with the membrane and enabling insertion. Once inside, the peptides are positioned between headgroups and lipid tails─a unique polar/apolar interface. Only one of two distinct orientations at this interface allows for the formation of the permeable "closed" conformation. In the closed conformation, the peptide crosses to the lower leaflet via another "anchoring" and flipping mechanism. Our findings provide atomistic insights into the permeation process of flexible cyclic peptides and reveal design considerations for each step of the process.

Development of an open-source software for isomer enumeration.

This article documents enu, a freely-downloadable, open-source and stand-alone program written in C++ for the enumeration of the constitutional isomers and stereoisomers of a molecular formula. The program relies on graph theory to enumerate all the constitutional isomers of a given formula on the basis of their canonical adjacency matrix. The stereoisomers of a given constitutional isomer are enumerated as well, on the basis of the automorphism group of this matrix. The isomer list is then reported in the form of canonical SMILES strings within files in XML format. The specification of the molecule family of interest is very flexible and the code is optimized for computational efficiency. The algorithms and implementations underlying enu are described, and simple illustrative applications are presented. The enu code is freely available on GitHub at https://github.com/csms-ethz/CombiFF .

Regularized by Physics: Graph Neural Network Parametrized Potentials for the Description of Intermolecular Interactions.

Simulations of molecular systems using electronic structure methods are still not feasible for many systems of biological importance. As a result, empirical methods such as force fields (FF) have become an established tool for the simulation of large and complex molecular systems. The parametrization of FF is, however, time-consuming and has traditionally been based on experimental data. Recent years have therefore seen increasing efforts to automatize FF parametrization or to replace FF with machine-learning (ML) based potentials. Here, we propose an alternative strategy to parametrize FF, which makes use of ML and gradient-descent based optimization while retaining a functional form founded in physics. Using a predefined functional form is shown to enable interpretability, robustness, and efficient simulations of large systems over long time scales. To demonstrate the strength of the proposed method, a fixed-charge and a polarizable model are trained on ab initio potential-energy surfaces. Given only information about the constituting elements, the molecular topology, and reference potential energies, the models successfully learn to assign atom types and corresponding FF parameters from scratch. The resulting models and parameters are validated on a wide range of experimentally and computationally derived properties of systems including dimers, pure liquids, and molecular crystals.

Predicting Collagen Triple Helix Stability through Additive Effects of Terminal Residues and Caps.

Collagen model peptides (CMPs) consisting of proline-(2S,4R)-hydroxyproline-glycine (POG) repeats have provided a breadth of knowledge of the triple helical structure of collagen, the most abundant protein in mammals. Predictive tools for triple helix stability have, however, lagged behind since the effect of CMPs with different frames ([POG]n , [OGP]n , or [GPO]n ) and capped or uncapped termini have so far been underestimated. Here, we elucidated the impact of the frame, terminal functional group and its charge on the stability of collagen triple helices. Combined experimental and theoretical studies with frame-shifted, capped and uncapped CMPs revealed that electrostatic interactions, strand preorganization, interstrand H-bonding, and steric repulsion at the termini contribute to triple helix stability. We show that these individual contributions are additive and allow for the prediction of the melting temperatures of CMP trimers.

Improving the IR spectra alignment algorithm with spectra deconvolution and combination with Raman or VCD spectroscopy.

The relative stereochemistry of organic molecules can be determined by comparing theoretical and experimental infrared (IR) spectra of all isomers and assessing the best match. For this purpose, we have recently developed the IR spectra alignment (IRSA) algorithm for automated optimal alignment. IRSA provides a set of quantitative metrics to identify the candidate structure that agrees best with the experimental spectrum. While the correct diastereomer could be determined for the tested sets of rigid and flexible molecules, two issues were identified with more complex compounds that triggered further development. First, strongly overlapping peaks in the IR spectrum are not treated adequately in the current IRSA implementation. Second, the alignment of multiple spectra from different sources (e.g. IR and VCD or Raman) can be improved. In this study, we present an in-depth discussion of these points, followed by the description of modifications to the IRSA algorithm to address them. In particular, we introduce the concept of deconvolution of the experimental and theoretical spectra with a set of pseudo-Voigt bands. The pseudo-Voigt bands have a set of parameters, which can be employed in the alignment algorithm, leading to improved scoring functions. We test the modified algorithm on two data sets. The first set contains compounds with IR and Raman spectra measured in this study, and the second set contains compounds with IR and VCD spectra available in the literature. We show that the algorithm is able to determine the correct diastereomer in all cases. The results highlight that vibrational spectroscopy can be a valuable alternative or complementary method to inform about the stereochemistry of compounds, and the performance of the updated IRSA algorithm suggests that it is a powerful tool for quantitative-based spectral assignments in academia and industry.